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Optomechanical systems attract a lot of attention because they provide a novel platform for quantum measurements, transduction, hybrid systems, and fundamental studies of quantum physics. Their classical nonlinear dynamics is surprisingly…
We consider the problem of reconstructing signals and images from periodic nonlinearities. For such problems, we design a measurement scheme that supports efficient reconstruction; moreover, our method can be adapted to extend to…
Topological photonics enables robust light manipulation with third-order optical nonlinearity, yet integrating second-order optical nonlinearity into a topological system faces fundamental challenges: frequency-dependent topological…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
Nonlinear dynamical systems possessing an invariant subspace in the phase space and chaotic or stochastic motion within the subspace often display on-off intermittency close to the threshold of stability of the subspace. In a class of…
Many present and future accelerators must operate with high intensity beams when distortions induced by space charge forces are among major limiting factors. Betatron tune depression of above approximately 0.1 per cell leads to significant…
Second-order nonlinear optical response allows to detect different properties of the system associated with the inversion symmetry breaking. Here, we use a second harmonic generation effect to investigate the alignment of a…
This paper develops a strong computational approach to simulate a three-dimensional nonlinear radiation-conduction model in optically thick media, subject to suitable initial and boundary conditions. The space derivatives are approximated…
One of the main applications of electromagnetic metasurfaces (MSs) is to tailor spatial field distributions. The radiation pattern of a given source can be desirably modified upon reflection on an MS having proper spatial modulation of its…
The engineering design process often relies on mathematical modeling that can describe the underlying dynamic behavior. In this work, we present a data-driven methodology for modeling the dynamics of nonlinear systems. To simplify this…
The recently developed generalized Fourier-Galerkin method is complemented by a numerical continuation with respect to the kinetic energy, which extends the framework to the investigation of modal interactions resulting in folds of the…
We demonstrate the phenomenon of stochastic resonance (SR) for discrete-time dynamical systems. We investigate various systems that are not necessarily bistable, but do have two well defined states, switching between which is aided by…
This work focuses on the development and analysis of a partitioned numerical method for moving domain, fluid-structure interaction problems. We model the fluid using incompressible Navier-Stokes equations, and the structure using linear…
In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…
This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The…
Studying 2 degree-of-freedom (DOF) Hamiltonian dynamical systems often involves the computation of stable & unstable manifolds of periodic orbits, due to the homoclinic & heteroclinic connections they can generate. Such study is generally…
Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the…
The discretization of the density matrix is proposed as a nonlinear positive map for systems with continuous variables. This procedure is used to calculate the entanglement between two modes through different criteria, such as Tsallis…
The quantitative determination of the order-chaos transition in a nonlinear dynamical system described by H\'enon mapping defined as $x[n+1]=1.0-A*x[n]^2+B*y[n], y[n+1]=B*x[n]$, where $B=0.3$, and $A$ is an adjustable control parameter, was…
We conduct an extensive study of nonlinear localized modes (NLMs), which are temporally periodic and spatially localized structures, in a two-dimensional array of repelling magnets. In our experiments, we arrange a lattice in a hexagonal…